Step 1: Recall what eddy currents are.
Eddy currents are circulating currents induced inside a bulk conductor whenever the magnetic flux through it changes with time.
Step 2: State the governing law.
Faraday's law gives the induced e.m.f. as $e = -\dfrac{d\phi}{dt}$, so a current appears only if $\dfrac{d\phi}{dt} \neq 0$.
Step 3: Test a plate in a steady field.
A steady magnetic field gives constant flux, so $\dfrac{d\phi}{dt} = 0$ and no eddy currents form. This rules out option (1).
Step 4: Test a coil in a steady field.
Again the field is steady, so no induction occurs, ruling out option (2).
Step 5: Test a steady current in a coil.
A constant current makes a constant field, so no change of flux and no eddy currents, ruling out option (3).
Step 6: Test a plate in a varying field.
A varying field changes the flux through the plate, inducing swirling eddy currents. So option (4) is correct.
\[ \boxed{\text{Thick metal plate in a varying magnetic field}} \]